15's Complement Subtraction Example B25C

4. Find Subtraction of B25C and C3B1 using 15's complement

Solution:

15's complement subtraction steps :

1. At first, find 15's complement of the B(subtrahend).
2. Then add it to the A(minuend).
3. If the final carry over of the sum is 1, then it is dropped and 1 is added to the result.
4. If there is no carry over, then 15's complement of the sum is the final result and it is negative.

Here A = B25C, B = C3B1.
Find A - B = ? using 15's complement
First find 15's complement of B = C3B1

Note : 15's complement of a number is obtained by subtracting each digit from F

Step-1: 15's complement of C3B1 is obtained by subtracting each digit from F



	F	F	F	F
-	C	3	B	1

	3	C	4	E

Step-2: Now Add this 3C4E to B25C

			1
	B	2	5	C
+	3	C	4	E

	E	E	A	A

Step by step solution of B25C + 3C4E = EEAA

Write the numbers, so that each digit lines up vertically


	B	2	5	C
+	3	C	4	E

Step-1 :
`=C_16+E_16`
`=12_10+14_10`
`=26_10`
`=16xx1+10`
`=1A_16`
Write the A in the sum place and carry the 1 to the next carry place

			1
	B	2	5	C
+	3	C	4	E

				A

Step-2 :
`=1+5_16+4_16`
`=1+5_10+4_10`
`=10_10`
`=A_16`
Write the A in the sum place

			1
	B	2	5	C
+	3	C	4	E

			A	A

Step-3 :
`=2_16+C_16`
`=2_10+12_10`
`=14_10`
`=E_16`
Write the E in the sum place

			1
	B	2	5	C
+	3	C	4	E

		E	A	A

Step-4 :
`=B_16+3_16`
`=11_10+3_10`
`=14_10`
`=E_16`
Write the E in the sum place

			1
	B	2	5	C
+	3	C	4	E

	E	E	A	A

Here there is no carry, answer is - (15's complement of the sum obtained EEAA)

Note : 15's complement of a number is obtained by subtracting each digit from F

Step-1: 15's complement of EEAA is obtained by subtracting each digit from F



	F	F	F	F
-	E	E	A	A

	1	1	5	5

So answer is -1155

This material is intended as a summary. Use your textbook for detail explanation.
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4. Example B25C - C3B1